## 51 Citations

### Nontrivial effective lower bounds for the least common multiple of a $q$-arithmetic progression

- Mathematics
- 2020

This paper is devoted to establish nontrivial effective lower bounds for the least common multiple of consecutive terms of a sequence ${(u_n)}_{n \in \mathbb{N}}$ whose general term has the form $u_n…

### Nontrivial effective lower bounds for the least common multiple of some quadratic sequences

- Mathematics
- 2020

This paper is devoted to studying the numbers $L_{c,m,n} := \mathrm{lcm}\{m^2+c ,(m+1)^2+c , \dots , n^2+c\}$, where $c,m,n$ are positive integers such that $m \leq n$. Precisely, we prove that…

### On the least common multiple of binary linear recurrence sequences

- MathematicsRocky Mountain Journal of Mathematics
- 2021

In this paper, we present a method for estimating the least common multiple of a large class of binary linear recurrence sequences. Let $P,Q,R_0$, and $R_1$ be fixed integers and let…

### Effective estimates for the least common multiple of some integer sequences

- Mathematics
- 2020

This thesis is devoted to studying estimates of the least common multiple of some integer sequences. Our study focuses on effective bounding of the $\mathrm{lcm}$ of some class of quadratic…

### New lower bounds for the least common multiples of arithmetic progressions

- Mathematics
- 2012

For relatively prime positive integers u0 and r, and for 0 ≤ k ≤ n, define uk:= u0 + kr. Let Ln:= lcm(u0, u1, ..., un) and let a, l ≥ 2 be any integers. In this paper, the authors show that, for…

### THE LEAST COMMON MULTIPLE OF CONSECUTIVE TERMS IN A QUADRATIC PROGRESSION

- MathematicsBulletin of the Australian Mathematical Society
- 2012

Abstract Let k be any given positive integer. We define the arithmetic function gk for any positive integer n by \[ g_{k}(n):=\frac {\prod _{i=0}^k ((n+i)^2+1)}{{\rm lcm}_{0\le i\le k}\{(n+i)^2+1\}}.…

### The least common multiple of consecutive arithmetic progression terms

- MathematicsProceedings of the Edinburgh Mathematical Society
- 2011

Abstract Let k ≥ 0, a ≥ 1 and b ≥ 0 be integers. We define the arithmetic function gk,a,b for any positive integer n by $$…

### A sharp upper bound for the sum of reciprocals of least common multiples

- MathematicsActa Mathematica Hungarica
- 2019

Let $$n$$ n and $$k$$ k be positive integers such that $$n\ge k+1$$ n ≥ k + 1 and let $$\{a_i\}_{i=1}^n$$ { a i } i = 1 n be an arbitrary given strictly increasing sequence of positive integers. Let…

## References

SHOWING 1-4 OF 4 REFERENCES

### On the Product of the Primes

- MathematicsCanadian Mathematical Bulletin
- 1972

In recent years several attempts have been made to obtain estimates for the product of the primes less than or equal to a given integer n. Denote by the above-mentioned product and define as usual…

### The Theory of Numbers

- Geology, EconomicsNature
- 1922

I FIND myself to-day in the same embarrassing position in which a predecessor of mine at Oxford found himself at Bradford in 1875, the president of a Section, probably the largest and most…

### On the produ t of the primes

- Canad . Math . Bull
- 1972